Rules for Well Temperament

[Billbrpt@aol.com]

In a message dated 98-02-06 10:40:50 EST, you write:

<< Dear Bill, 
 I don't want to ask what may be an obvious question, but what are the rules
 for Well-Temperament?
    I know that Equal Temperament is supposed to have pur unisons, octaves
stretched to a lesser or greater amount, fifths that are contracted slightly
from pure (about 1/2 a beat), fourths that are expanded from pure (about 1
beat), and thirds, sixths, tenths, etc. that progress evenly and slightly
increase in speed as you play up the scale.
   But, I don't know what the rules for Well-Temperament are.  I have never
heard of that.
  Would you mind responding? >>

    I do not mind at all responding.  Please never feel that any question is
too obvious or naive to ask.  I just responded yesterday to a question about
my phrase, "Cycle of 5ths based tuning".  It is essentially the same question.
You can find the "Rules for a Well-Tempered tuning in Owen Jorgensen's second
publication, "A Handbook for Tuning Harpsichords and Fortepianos".  These
"Rules" were written by Andreas Werkmeister for whom some well-known WT's are
named.  Here is a copy of that part of my post:

  <<The idea comes from the rules that Andreas Werkmeister wrote for a Well-
Tempered tuning (WT) (also called Well-Temperament).  To paraphrase these
rules, a WT must have its slowest beating 3rd at C  (the "top" of the cycle).
As you add either sharps or flats, the speed of the 3rds increase in alignment
with the cycle, not chromatically.  There can be no "imbalances" in the
Temperament.  The 3rd of the key of A cannot beat faster than the 3rd for the
key of E, for example.  There can be two or more in a row that are the same
but they must ultimately progress to being fastest at F#, the "bottom" of the
cycle. >>

     Additionally, the rules state that all  4ths & 5ths are to be either pure
or tempered wide or narrow, respectively.  The pure 4ths & 5ths are generally
found among the black keys and the tempered among the whites but there can be
exceptions.

    The beating of the 3rds can range from pure to nearly the speed of an ET
3rd starting with the note C.  The slower the 3rd is at C, the faster the 3rd
will beat at F#.  A very mild WT can be created by starting only slightly
slower than the speed of an ET 3rd.  Most Victorian C4-E4 3rds will beat at 4
bps.

    Perhaps someone will be willing to copy The "Rules for WT" by Werkmeister
and post them on this List for those who do not have access to Owen's
publication and are curious about these "Rules".

    Bill Bremmer RPT
    Madison, Wisconsin